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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 24643, 10 pages
http://dx.doi.org/10.1155/JAMSA/2006/24643

Large-scale stochastic hereditary systems under Markovian structural perturbations. Part III. Qualitative analysis

Department of Mathematics, The University of Texas at Arlington, Arlington 76019, TX, USA

Received 14 January 2005; Revised 26 October 2005; Accepted 26 October 2005

Copyright © 2006 G. S. Ladde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this final part of the work, the convergence and stability analysis of large-scale stochastic hereditary systems under random structural perturbations is investigated. This is achieved through the development and the utilization of comparison theorems in the context of vector Lyapunov-like functions and decomposition-aggregation method. The byproduct of the investigation suggests that the qualitative properties of decoupled stochastic hereditary subsystems under random structural perturbations are preserved, as long as the self-inhibitory effects of subsystems are larger than cross-interaction effects of the subsystems. Again, it is shown that these properties are affected by hereditary and random structural perturbations effects. It is further shown that the mathematical conditions are algebraically simple, and are robust to the parametric changes. Moreover, the work generates a concept of block quasimonotone nondecreasing property that is useful for the investigation of hierarchic systems. These results are further extended to the integrodifferential equations of Fredholm type.